Vitamins A,D,E,K are fat soluble vitamins. Can be found in dark green leafy vegetables. Vitamin D CAN be supplemented, but its main function is to promote calcium uptake in bone.I am trying to get my eggs to carry vitamin D, E, K, and A which is known to be present on dark orange yolk but feeding the birds marigold or some other form of color enhancements, those vitamins don't exist
I don't see why one would need to supplement D.
Make a chicken garden with spinach, kale, chard. Also look at colorful winter squashes.
In winter you can look into sprouting seeds for daily treats.